A survey on the missing Moore graph

This is a survey on some known properties of the possible Moore graph (or graphs) ¿ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ¿ induced by a vertex subset C, the following graphs are distance-regular:...

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Detalhes bibliográficos
Autor: Dalfó Simó, Cristina|||0000-0002-8438-9353
Formato: artículo
Fecha de publicación:2019
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/127212
Acesso em linha:https://hdl.handle.net/2117/127212
https://dx.doi.org/10.1016/j.laa.2018.12.035
Access Level:acceso abierto
Palavra-chave:Graph theory
Matrices
Moore graphs
Distance-regular graph
Outindependent graph
Spectral graph theory
Automorphisms
Grafs, Teoria de
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
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oai_identifier_str oai:upcommons.upc.edu:2117/127212
network_acronym_str ES
network_name_str España
repository_id_str
spelling A survey on the missing Moore graphDalfó Simó, Cristina|||0000-0002-8438-9353Graph theoryMatricesMoore graphsDistance-regular graphOutindependent graphSpectral graph theoryAutomorphismsGrafs, Teoria deAnàlisi combinatòriaÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsThis is a survey on some known properties of the possible Moore graph (or graphs) ¿ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ¿ induced by a vertex subset C, the following graphs are distance-regular: The induced graph of the vertices at distance 1 from C when C is a set of 400 independent vertices; the induced graphs of the vertices at distance 2 from C when C is a vertex or an edge, and the line graph of ¿. Besides, ¿ is an edge-distance-regular graph.Peer ReviewedElsevier20192019-01-0120192019-01-18journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/127212https://dx.doi.org/10.1016/j.laa.2018.12.035reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1272122026-05-27T15:37:01Z
dc.title.none.fl_str_mv A survey on the missing Moore graph
title A survey on the missing Moore graph
spellingShingle A survey on the missing Moore graph
Dalfó Simó, Cristina|||0000-0002-8438-9353
Graph theory
Matrices
Moore graphs
Distance-regular graph
Outindependent graph
Spectral graph theory
Automorphisms
Grafs, Teoria de
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
title_short A survey on the missing Moore graph
title_full A survey on the missing Moore graph
title_fullStr A survey on the missing Moore graph
title_full_unstemmed A survey on the missing Moore graph
title_sort A survey on the missing Moore graph
dc.creator.none.fl_str_mv Dalfó Simó, Cristina|||0000-0002-8438-9353
author Dalfó Simó, Cristina|||0000-0002-8438-9353
author_facet Dalfó Simó, Cristina|||0000-0002-8438-9353
author_role author
dc.subject.none.fl_str_mv Graph theory
Matrices
Moore graphs
Distance-regular graph
Outindependent graph
Spectral graph theory
Automorphisms
Grafs, Teoria de
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
topic Graph theory
Matrices
Moore graphs
Distance-regular graph
Outindependent graph
Spectral graph theory
Automorphisms
Grafs, Teoria de
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
description This is a survey on some known properties of the possible Moore graph (or graphs) ¿ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ¿ induced by a vertex subset C, the following graphs are distance-regular: The induced graph of the vertices at distance 1 from C when C is a set of 400 independent vertices; the induced graphs of the vertices at distance 2 from C when C is a vertex or an edge, and the line graph of ¿. Besides, ¿ is an edge-distance-regular graph.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2019
2019-01-18
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/127212
https://dx.doi.org/10.1016/j.laa.2018.12.035
url https://hdl.handle.net/2117/127212
https://dx.doi.org/10.1016/j.laa.2018.12.035
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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